PRICING SUPPLEMENT NO. 33 Rule 424(b)(3) DATED: September 1, 2004 File No. 333-109793 (To Prospectus dated November 17, 2003, and Prospectus Supplement dated November 17, 2003) $10,668,950,162 THE BEAR STEARNS COMPANIES INC. Medium-Term Notes, Series B Principal Amount: $5,000,000 Floating Rate Notes [x] Book Entry Notes [x] Original Issue Date: 9/24/2004 Fixed Rate Notes [ ] Certificated Notes [ ] Maturity Date: 9/24/2009 CUSIP#: 073928G72 Option to Extend Maturity: No [x] Yes [ ] Final Maturity Date: Minimum Denominations: $100,000, increased in multiples of $10,000 Optional Optional Redemption Repayment Repayment Redeemable On Price(s) Date(s) Price(s) ------------- ---------- --------- --------- N/A N/A N/A N/A Applicable Only to Fixed Rate Notes: ----------------------------------- Interest Rate: Interest Payment Dates: Applicable Only to Floating Rate Notes: -------------------------------------- Interest Rate Basis: Maximum Interest Rate: N/A [ ] Commercial Paper Rate Minimum Interest Rate: N/A [ ] Federal Funds Effective Rate [ ] Federal Funds Open Rate Interest Reset Date(s): * [ ] Treasury Rate Interest Reset Period: Monthly [ ] LIBOR Reuters Interest Payment Date(s): ** [ ] LIBOR Telerate Interest Determination Date(s): *** [ ] Prime Rate [x] CMT Rate+ Multiplier: 0.715 Initial Interest Rate: [TBD]% Interest Payment Period: Monthly Index Maturity: Ten Years Spread (plus or minus): N/A * On the 24th of each month prior to Maturity. ** On the 24th of each month, including the maturity date. *** On the second Business Day prior to each Interest Reset Date. + The Interest Rate for each Interest Payment Period shall be determined by the Calculation Agent in accordance with the following formula: (10 Year CMT Rate) x (Multiplier) Where: 10 Year CMT Rate = the 10 Year CMT Rate displayed on CMT Telerate page 7051 Multiplier = 0.715 The distribution of Notes will conform to the requirements set forth in Rule 2720 of the NASD Conduct Rules. -2-